In some fanfictions, if they survived, they might have changed the whole course of the wizarding war. They could have joined forces with other powerful wizards and witches earlier and potentially prevented Voldemort from gaining as much power as he did in the original story. They might have also influenced the Hogwarts curriculum, emphasizing more on defensive magic against the Dark Arts from an earlier stage.
One possibility could be that there was some sort of magical interference. Maybe a powerful magical artifact or a spell was in place that deflected the Killing Curse just enough for James to survive. For example, if there was a hidden protection charm on him that he wasn't aware of.
Well, a great James Potter survived fanfiction is 'James Potter's Redemption Arc'. It could explore how his survival changes his perspective on life and death. Maybe he has to deal with the guilt of leaving his family behind in the first place. Then there's 'The Return of James Potter'. This one might show his struggles to fit back into the wizarding world he once knew, as so much has changed since his supposed death.
Perhaps James had some hidden magical ability that he was unaware of until that moment. It could be something that was passed down through his family but had never manifested before. This ability could have protected him from Voldemort's killing curse. Or, it's possible that there was a plot by some other characters to save James. There could have been a group of wizards or witches who had been secretly working to keep James alive because they knew his importance in the fight against Voldemort. They might have used some sort of time - turning magic or a protective charm that Voldemort couldn't break through.
The relationship between Harry and his parents would be completely different. He would grow up with their love and guidance, rather than feeling like an orphan. There would be a much stronger family bond.
One interesting plot could be that James, having survived, decides to go into hiding with his family in a more secretive way. He uses his survival as a motivation to become a stronger wizard and starts to train secretly, waiting for the right moment to face Voldemort again.
Well, if James Potter survived, it would completely change the backstory of Harry Potter. For one thing, Harry might have grown up with his father, which would have meant a very different childhood for him. He wouldn't be the orphan raised by the Dursleys. Also, James Potter was a talented wizard, so he could have been a major influence on Harry's magical education from a very young age. This would likely make Harry even more powerful and confident earlier on. And the fight against Voldemort would have been different too, as James would have been another powerful force against the Dark Lord right from the start.
Harry's character development would be significantly different. With his parents alive, he would be exposed to a more stable family environment. His magical education could start earlier and be more comprehensive as he learns from two powerful wizards. This could make him more powerful and less impulsive. Instead of seeking validation from others like he did at Hogwarts in the original story, he would have the unconditional love of his parents, which could shape him into a more well - rounded and less angst - ridden character. For example, he might not have had such a strong urge to prove himself in dangerous situations.
One possible plotline could be that Voldemort's attack on the Potter family fails in a different way. Maybe James uses a powerful, unknown spell that deflects Voldemort's killing curse. As a result, Lily and James go into hiding with Harry. They might then start to form an underground resistance against Voldemort, using their knowledge of the Dark Lord's weaknesses. This could lead to a completely different wizarding war, with the Potters at the forefront, and Harry growing up with his parents by his side, learning magic from them directly.
Yes, there are quite a few. You can start by looking on platforms like Archive of Our Own. Some fanfictions in this category explore how her survival would change the entire Harry Potter storyline, with her being able to directly influence Harry's upbringing and the fight against Voldemort.